The sum of two numbers is $136$, and their difference is $4$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 136}$ ${x-y = 4}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 140 $ $ x = \dfrac{140}{2} $ ${x = 70}$ Now that you know ${x = 70}$ , plug it back into $ {x+y = 136}$ to find $y$ ${(70)}{ + y = 136}$ ${y = 66}$ You can also plug ${x = 70}$ into $ {x-y = 4}$ and get the same answer for $y$ ${(70)}{ - y = 4}$ ${y = 66}$ Therefore, the larger number is $70$, and the smaller number is $66$.